The angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky is 76degree.If the horizontal distance between the building and the hot air balloon is 354feet, find the height of the air balloon.
Accepted Solution
A:
Answer: [tex]1,514.816\ feet[/tex]Step-by-step explanation: See the image attached, where "x" represents the height in feet of the hot air balloon. Notice that: [tex]x=95+BC[/tex] To find the lenght of the side BC of the right triangle, you need to use the following Trigonometric Identity: [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] Observe that: [tex]\alpha =76\°\\opposite=BC\\adjacent=AC=354[/tex] Substituting values and solving for "BC", you get: [tex]tan(76\°)=\frac{BC}{354}\\\\(tan(76\°))(354)=BC\\\\BC=1,419.816[/tex] Therefore "x" is: [tex]x=95+1,419.816\\\\x=1,514.816[/tex]